Question

Find the area of the region bounded by the following curves, X-axis and the given lines : y² = x, x = 0, x = 4

Answer 1

The required area consists of two bounded regions A₁ and A₂ which are equal in areas.
For y² = x, y = `sqrt(x)`
Required area = A₁ + A₂ = 2A₁

= `2int_0^4 y*dx,  "where"  y = sqrt(x)`

= `2int_0^4 sqrt(x)*dx`

= `2[(x^(3/2))/(3/2)]_0^4`

= `2[2/3(4)^(3/2) - 0]`

= `2[2/3(2^2)^(3/2)]`

= `(32)/(3) "sq units"`.